UV index measurement and model agreement: uncertainties and limitations

En les últimes dècades, l'increment dels nivells de radiació solar ultraviolada (UVR) que arriba a la Terra (principalment degut a la disminució d'ozó estratosfèric) juntament amb l'augment detectat en malalties relacionades amb l'exposició a la UVR, ha portat a un gran volum d'investigacions sobre la radiació solar en aquesta banda i els seus efectes en els humans. L'índex ultraviolat (UVI), que ha estat adoptat internacionalment, va ser definit amb el propòsit d'informar al públic general sobre els riscos d'exposar el cos nu a la UVR i per tal d'enviar missatges preventius. L'UVI es va definir inicialment com el valor màxim diari. No obstant, el seu ús actual s'ha ampliat i té sentit referir-se a un valor instantani o a una evolució diària del valor d'UVI mesurat, modelitzat o predit. El valor concret d'UVI està afectat per la geometria Sol-Terra, els núvols, l'ozó, els aerosols, l'altitud i l'albedo superficial. Les mesures d'UVI d'alta qualitat són essencials com a referència i per estudiar tendències a llarg termini; es necessiten també tècniques acurades de modelització per tal d'entendre els factors que afecten la UVR, per predir l'UVI i com a control de qualitat de les mesures. És d'esperar que les mesures més acurades d'UVI s'obtinguin amb espectroradiòmetres. No obstant, com que els costs d'aquests dispositius són elevats, és més habitual trobar dades d'UVI de radiòmetres eritemàtics (de fet, la majoria de les xarxes d'UVI estan equipades amb aquest tipus de sensors). Els millors resultats en modelització s'obtenen amb models de transferència radiativa de dispersió múltiple quan es coneix bé la informació d'entrada. No obstant, habitualment no es coneix informació d'entrada, com per exemple les propietats òptiques dels aerosols, la qual cosa pot portar a importants incerteses en la modelització. Sovint, s'utilitzen models més simples per aplicacions com ara la predicció d'UVI o l'elaboració de mapes d'UVI, ja que aquests són més ràpids i requereixen menys paràmetres d'entrada. Tenint en compte aquest marc de treball, l'objectiu general d'aquest estudi és analitzar l'acord al qual es pot arribar entre la mesura i la modelització d'UVI per condicions de cel sense núvols. D'aquesta manera, en aquest estudi es presenten comparacions model-mesura per diferents tècniques de modelització, diferents opcions d'entrada i per mesures d'UVI tant de radiòmetres eritemàtics com d'espectroradiòmeters. Com a conclusió general, es pot afirmar que la comparació model-mesura és molt útil per detectar limitacions i estimar incerteses tant en les modelitzacions com en les mesures. Pel que fa a la modelització, les principals limitacions que s'han trobat és la falta de coneixement de la informació d'aerosols considerada com a entrada dels models. També, s'han trobat importants diferències entre l'ozó mesurat des de satèl·lit i des de la superfície terrestre, la qual cosa pot portar a diferències importants en l'UVI modelitzat. PTUV, una nova i simple parametrització pel càlcul ràpid d'UVI per condicions de cel serens, ha estat desenvolupada en base a càlculs de transferència radiativa. La parametrització mostra una bona execució tant respecte el model base com en comparació amb diverses mesures d'UVI. PTUV ha demostrat la seva utilitat per aplicacions particulars com ara l'estudi de l'evolució anual de l'UVI per un cert lloc (Girona) i la composició de mapes d'alta resolució de valors d'UVI típics per un territori concret (Catalunya). En relació a les mesures, es constata que és molt important saber la resposta espectral dels radiòmetres eritemàtics per tal d'evitar grans incerteses a la mesura d'UVI. Aquest instruments, si estan ben caracteritzats, mostren una bona comparació amb els espectroradiòmetres d'alta qualitat en la mesura d'UVI. Les qüestions més importants respecte les mesures són la calibració i estabilitat a llarg termini. També, s'ha observat un efecte de temperatura en el PTFE, un material utilitzat en els difusors en alguns instruments, cosa que potencialment podria tenir implicacions importants en el camp experimental. Finalment, i pel que fa a les comparacions model-mesura, el millor acord s'ha trobat quan es consideren mesures d'UVI d'espectroradiòmetres d'alta qualitat i s'usen models de transferència radiativa que consideren les millors dades disponibles pel que fa als paràmetres òptics d'ozó i aerosols i els seus canvis en el temps. D'aquesta manera, l'acord pot ser tan alt dins un 0.1º% en UVI, i típicament entre menys d'un 3%. Aquest acord es veu altament deteriorat si s'ignora la informació d'aerosols i depèn de manera important del valor d'albedo de dispersió simple dels aerosols. Altres dades d'entrada del model, com ara l'albedo superficial i els perfils d'ozó i temperatura introdueixen una incertesa menor en els resultats de modelització.

Modelling, control and supervision for a class of hybrid systems

The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.